On the Critical Resolved Shear Stress and its Importance in the Fatigue Performance of Steels and other Metals with Different Crystallographic Structures
M. Mlikota, S. Schmauder
This study deals with the numerical estimation of the fatigue life represented in the form of strength-life (S-N, or Wöhler) curves of metals with different crystallographic structures, namely body-centered cubic (BCC) and face-centered cubic (FCC). Their life curves are determined by analyzing the initiation of a short crack under the influence of microstructure and subsequent growth of the long crack, respectively. Micro-models containing microstructures of the materials are set up by using the finite element method (FEM) and are applied in combination with the Tanaka-Mura (TM) equation in order to estimate the number of cycles required for the crack initiation. The long crack growth analysis is conducted using the Paris law. The study shows that the crystallographic structure is not the predominant factor that determines the shape and position of the fatigue life curve in the S-N diagram, but it is rather the material parameter known as the critical resolved shear stress (CRSS). Even though it is an FCC material, the investigated austenitic stainless steel AISI 304 shows an untypically high fatigue limit (208 MPa), which is higher than the fatigue limit of the BCC vanadium-based micro-alloyed forging steel AISI 1141 (152 MPa).
Keywords
Fatigue, Fatigue Life Curves, Numerical Analysis, Microstructure, Crystallographic Structure, Critical Resolved Shear Stress, Fatigue Limit
Published online , 29 pages
Citation: M. Mlikota, S. Schmauder, On the Critical Resolved Shear Stress and its Importance in the Fatigue Performance of Steels and other Metals with Different Crystallographic Structures, Materials Research Foundations, Vol. 114, pp 37-65, 2022
DOI: https://doi.org/10.21741/9781644901656-3
Part of the book on Multiscale Fatigue Modelling of Metals
References
[1] Budynas R.G, Nisbett J.K, 2015, Fatigue failure resulting from variable loading. In Shigley’s Mechanical Engineering Design, 10th ed, McGraw-Hill Education: New York, NY, USA,; pp. 273–349, ISBN 978-0-07-339820-4.
[2] Ferro A, Montalenti G,1964, On the effect of the crystalline structure on the form of fatigue curves. Philos. Mag., 10, 1043. https://doi.org/10.1080/14786436508218923
[3] Ferro A, Mazzetti P, Montalenti G, 1965, On the effect of the crystalline structure on fatigue: Comparison between body-centred metals (Ta, Nb, Mo and W) and face-centred and hexagonal metals. Phil. Mag. J. Theor. Exp. Appl. Phys., 12, 867–875. https://doi.org/10.1080/14786436508218923
[4] Buck A, 1967, Fatigue properties of pure metals, Int. J. Fract. Mech. 3, 145–152. https://doi.org/10.1007/BF00182692
[5] Grosskreutz J.C, 1971, Fatigue mechanisms in the sub-creep range. ASTM ,495, 5–60. https://doi.org/10.1520/STP26684S
[6] Rogne B, Thaulow C, 2015, Strengthening mechanisms of iron micropillars. Phil. Mag., 95, 1814–1828. https://doi.org/10.1080/14786435.2014.984004
[7] Uchic M.D, Dimiduk D.M, Florando J.N, Nix W.D, 2004, Sample dimensions Influence strength and crystal plasticity. Science, 305, 986–989. https://doi.org/10.1126/science.1098993
[8] Kunz A, Pathak S, Greer J.R, 2011, Size effects in Al nanopillars: Single crystalline vs. bicrystalline. Acta Mater., 59, 4416–4424. https://doi.org/10.1016/j.actamat.2011.03.065
[9] Greer J.R, Hosson J.T.D, 2011, Plasticity in small-sized metallic systems: Intrinsic versus extrinsic size effect. Prog. Mater Sci., 56, 654–724. https://doi.org/10.1016/j.pmatsci.2011.01.005
[10] Chen Z.M, Okamoto N.L, Demura M, Inui H, 2016, Micropillar compression deformation of single crystals of Co3(Al,W) with the L12 structure. Scr. Mater., 121, 28–31. https://doi.org/10.1016/j.scriptamat.2016.04.029
[11] Monnet G, Pouchon M.A, 2013, Determination of the critical resolved shear stress and the friction stress in austenitic stainless steels by compression of pillars extracted from single grains. Mater. Lett. 98, 128–130. https://doi.org/10.1016/j.matlet.2013.01.118
[12] Dimiduk D.M, Woodward C, LeSar R, Uchic M.D, 2006, Scale-free intermittent flow in crystal plasticity, Science 312, 1188–1190. https://doi.org/10.1126/science.1123889
[13] Csikor F.F, Motz C, Weygand D, Zaiser M, Zapperi S, 2007, Dislocation Avalanches, Strain Bursts, and the Problem of Plastic Forming at the Micrometer Scale. Science, 318, 251–254. https://doi.org/10.1126/science.1143719
[14] Okamoto N.L, Kashioka D, Inomoto M, Inui H, Takebayashi H, Yamaguchi S, 2013, Compression deformability of gamma- and zeta-Fe-Zn intermetallics to mitigate detachment of brittle intermetallic coating of galvannealed steels. Scr. Mater. 69, 307–310. https://doi.org/10.1016/j.scriptamat.2013.05.003
[15] Okamoto N.L, Fujimoto S, Kambara Y, Kawamura M, Chen Z.M.T, Matsunoshita H, Tanaka K, Inui H, George E.P, 2016, Size effect, critical resolved shear stress, stacking fault energy, and solid solution strengthening in the CrMnFeCoNi high-entropy alloy. Sci. Rep. 6, 35863. https://doi.org/10.1038/srep35863
[16] Kiener D, Motz C, Schöberl T, Jenko M, Dehm G, 2006, Determination of mechanical properties of copper at the micron scale. Adv. Eng. Mater. 8, 1119–1125. https://doi.org/10.1002/adem.200600129
[17] Jennings A.T, Burek M.J, Greer J.R, 2010, Microstructure versus Size: Mechanical properties of electroplated single crystalline Cu nanopillars. Phys. Rev. Lett. 104, 135503. https://doi.org/10.1103/PhysRevLett.104.135503
[18] Schneider A.S, Kaufmann D, Clark B.G, Frick C.P, Gruber P.A, Mцnig R, Kraft O, Arzt E, 2009, Correlation between critical temperature and strength of small-scale bcc pillars. Phys. Rev. Lett. 103, 105501. https://doi.org/10.1103/PhysRevLett.103.105501
[19] Dimiduk D, Uchic M, Parthasarathy T, 2005, Size-affected single-slip behavior of pure nickel microcrystals. Acta Mater. 53, 4065–4077. https://doi.org/10.1016/j.actamat.2005.05.023
[20] Greer J.R, Oliver W.C, Nix W.D, 2004, Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients. Acta Mater. 2005, 53, 1821–1830. https://doi.org/10.1016/j.actamat.2004.12.031
[21] Shade P, Uchic M, Dimiduk D, Viswanathan G, Wheeler R, Fraser H, 2011, Size-affected single-slip behavior of Rene N5 microcrystals. Mater. Sci. Eng. A 2012, 535, 53–61. https://doi.org/10.1016/j.msea.2011.12.041
[22] Okamoto N.L, Kashioka D, Hirato T, Inui H, 2014, Specimen- and grain-size dependence of compression deformation behavior in nanocrystalline copper. Int. J. Plast. 56, 173–183. https://doi.org/10.1016/j.ijplas.2013.12.003
[23] Okamoto N.L, Inomoto M, Adachi, H, Takebayashi, H, Inui H, 2014, Micropillar compression deformation of single crystals of the intermetallic compound zeta-FeZn13. Acta Mater. 65, 229–239. https://doi.org/10.1016/j.actamat.2013.10.065
[24] Zheng H, Cao A, Weinberger C.R, Huang J.Y, Du K, Wang J, Ma Y, Xia Y, Mao S.X, 2010, Discrete plasticity in sub-10-nm-sized gold crystals. Nat. Commun. 1, 144. https://doi.org/10.1038/ncomms1149
[25] Greer J.R, Weinberger C.R, Cai W, 2008, Comparing the strength of f.c.c. and b.c.c. sub-micrometer pillars: Compression experiments and dislocation dynamics simulations. Mater. Sci. Eng. A 493, 21–25. https://doi.org/10.1016/j.msea.2007.08.093
[26] Schneider A, Clark B, Frick C, Gruber P, Arzt E, 2009, Effect of orientation and loading rate on compression behavior of small-scale Mo pillars. Mater. Sci. Eng. A 508, 241–246. https://doi.org/10.1016/j.msea.2009.01.011
[27] Hagen A, Thaulow C, 2016, Low temperature in-situ micro-compression testing of iron pillars, Mater. Sci. Eng. A 678, 355–364. https://doi.org/10.1016/j.msea.2016.09.110
[28] Bruesewitz C, Knorr I, Hofsaess H, Barsoum M.W, Volkert C.A, 2013, Single crystal pillar microcompression tests of the MAX phases Ti2InC and Ti4AlN3, Scr. Mater. 69, 303–306. https://doi.org/10.1016/j.scriptamat.2013.05.002
[29] Feller-Kniepmeier M, Hundt M, 1983, Deformation properties of high purity alpha-Fe single crystals. Scr. Metall. 17, 905–908. https://doi.org/10.1016/0036-9748(83)90259-4
[30] Stein D, Low J, Seybolt A, 1963, The mechanical properties of iron single crystals containing less than 5 × 10−3 ppm carbon. Acta Metall. 11, 1253–1262. https://doi.org/10.1016/0001-6160(63)90114-7
[31] Stein D.F, Low J.R, 1966, Effects of orientation and carbon on the mechanical properties of iron single crystals. Acta Metall. 14, 1183–1194. https://doi.org/10.1016/0001-6160(66)90236-7
[32] Guo E.-Y, Xie H X, Singh S. S, Kirubanandham A, Jing T, Chawla N, 2014, Mechanical characterization of microconstituents in a cast duplex stainless steel by micropillar compression. Mater. Sci. Eng. A 598, 98–105. https://doi.org/10.1016/j.msea.2014.01.002
[33] Cruzado A, Gan B, Jimenez M, Barba D, Ostolaza K, Linaza A, Molina-Aldareguia J, Llorca J, Segurado J, 2015, Multiscale modeling of the mechanical behavior of IN718 superalloy based on micropillar compression and computational homogenization. Acta Mater. 98, 242–253. https://doi.org/10.1016/j.actamat.2015.07.006
[34] Jin H.H, Ko E, Kwon J, Hwang S.S, Shin C, 2016, Evaluation of critical resolved shear strength and deformation mode in proton-irradiated austenitic stainless steel using micro-compression tests. J. Nucl. Mater. 470, 155–163. https://doi.org/10.1016/j.jnucmat.2015.12.029
[35] Wu J, Tsai W, Huang J, Hsieh C, Huang G.-R, 2016, Sample size and orientation effects of single crystal aluminum. Mater. Sci. Eng. A 662, 296–302. https://doi.org/10.1016/j.msea.2016.03.076
[36] Palomares Garcia A.J, Perez-Prado M.T, Molina-Aldareguia J.M, 2017, Effect of lamellar orientation on the strength and operating deformation mechanisms of fully lamellar TiAl alloys determined by micropillar compression. Acta Mater. 123, 102–114. https://doi.org/10.1016/j.actamat.2016.10.034
[37] Campos M, Bautista A, Caceres D, Abenojar J, Torralba J, 2003, Study of the interfaces between austenite and ferrite grains in P/M duplex stainless steels. J. Eur. Ceram. Soc. 23, 2813–2819. https://doi.org/10.1016/S0955-2219(03)00293-0
[38] Ramazani A, Mukherjee K, Prahl U, Bleck W, 2012, Modelling the effect of microstructural banding on the flow curve behaviour of dual-phase (DP) steels. Comput. Mater. Sci. 52, 46–54. https://doi.org/10.1016/j.commatsci.2011.05.041
[39] Hocker S, Schmauder S, Bakulin A.V, Kulkova S.E, 2014, Ab initio investigation of tensile strengths of metal(1 1 1)/alpha-Al2O3(0 0 0 1) interfaces. Philos. Mag. 94, 265–284. https://doi.org/10.1080/14786435.2013.852288
[40] Kulkova S.E, Bakulin A.V, Kulkov S.S, Hocker S, Schmauder S, 2015, Influence of interstitial impurities on the Griffith work in Ti-based alloys. Phys. Scr. 90, 094010. https://doi.org/10.1088/0031-8949/90/9/094010
[41] Bakulin A.V, Spiridonova T, Kulkova S.E, Hocker S, Schmauder, S, 2016, Hydrogen diffusion in doped and undoped alpha-Ti: An ab-initio investigation. Int. J. Hydrogen Energy 41, 9108–9116. https://doi.org/10.1016/j.ijhydene.2016.03.192
[42] Kohler C, Kizler P, Schmauder S, 2005, Atomistic simulation of precipitation hardening in alpha-iron: Influence of precipitate shape and chemical composition. Modell. Simul. Mater. Sci. Eng. 13, 35–45. https://doi.org/10.1088/0965-0393/13/1/003
[43] Prskalo A.P, Schmauder S, Ziebert C, Ye J, Ulrich S, 2010, Molecular dynamics simulations of the sputtering of SiC and Si3N4. Surf. Coat. Technol. 204, 2081–2084. https://doi.org/10.1016/j.surfcoat.2009.09.043
[44] Prskalo A.-P, Schmauder S, Ziebert C, Ye J, Ulrich S, 2011, Molecular dynamics simulations of the sputtering process of silicon and the homoepitaxial growth of a Si coating on silicon. Comput. Mater. Sci. 50, 1320–1325. https://doi.org/10.1016/j.commatsci.2010.08.006
[45] Bozic Z, Schmauder S, Mlikota M, Hummel M, 2014, Multiscale fatigue crack growth modelling for welded stiffened panels. Fatigue Fract. Eng. Mater. Struct., 37, 1043–1054. https://doi.org/10.1111/ffe.12189
[46] Bozic Z, Schmauder S, Mlikota M, Hummel M, 2018, Multiscale fatigue crack growth modeling for welded stiffened panels. In Handbook of Mechanics of Materials, Schmauder S, Chen C.-S, Chawla, K.K, Chawla N, Chen W, Kagawa Y, Eds, Springer: Singapore, pp. 1–21, ISBN 978-981-10-6855-3. https://doi.org/10.1007/978-981-10-6855-3_73-1
[47] Tanaka K, Mura T,1981, A dislocation model for fatigue crack initiation. J. Appl. Mech. 48, 97–103. https://doi.org/10.1115/1.3157599
[48] Tanaka K, Mura T, 1982, A theory of fatigue crack initiation at inclusions. Metall. Trans. A ,13, 117–123. https://doi.org/10.1007/BF02642422
[49] Mlikota M, Staib S, Schmauder S, Bozic Z. 2017, Numerical determination of Paris law constants for carbon steel using a two-scale model. J. Phys. Conf. Ser. 843, 012042. https://doi.org/10.1088/1742-6596/843/1/012042
[50] Mlikota M, Schmauder S, Bozic Z, Hummel M, 2017, Modelling of overload effects on fatigue crack initiation in case of carbon steel. Fatigue Fract. Eng. Mater. Struct. 40, 1182–1190. https://doi.org/10.1111/ffe.12598
[51] Mlikota M, Schmauder S, 2017, Numerical determination of component Woehler curve. DVM Bericht 1684, 111–124
[52] Mlikota M, Schmauder S, Bozic Z, 2018, Calculation of the Woehler (S-N) curve using a two-scale model. Int. J. Fatigue 114, 289–297. https://doi.org/10.1016/j.ijfatigue.2018.03.018
[53] ABAQUS, version 2018, Abaqus Documentation, Simulia: Providence, RI, USA,.
[54] Socie D.F. 1996, Fatigue damage simulation models for multiaxial loading. In Proceedings of the Sixth International Fatigue Congress (Fatigue ’96), Berlin, Germany, 6–10 May; pp. 967–976. https://doi.org/10.1016/B978-008042268-8/50038-1
[55] Glodez S, Jezernik N, Kramberger J, Lassen T, 2010, Numerical modelling of fatigue crack initiation of martensitic steel. Adv. Eng. Software 2010, 41, 823–829. https://doi.org/10.1016/j.advengsoft.2010.01.002
[56] Jezernik N, Kramberger J, Lassen T, Glodez S, 2010, Numerical modelling of fatigue crack initiation and growth of martensitic steels. Fatigue Fract. Eng. Mater. Struct. 33, 714–723. https://doi.org/10.1111/j.1460-2695.2010.01482.x
[57] Huang X, Brueckner-Foit A, Besel M, Motoyashiki Y, 2007, Simplified three-dimensional model for fatigue crack initiation. Eng. Fract. Mech. 74, 2981–2991. https://doi.org/10.1016/j.engfracmech.2006.05.027
[58] Briffod F, Shiraiwa T, Enoki M, 2016, Fatigue crack initiation simulation in pure iron polycrystalline aggregate. Mater. Trans. 57, 1741–1746. https://doi.org/10.2320/matertrans.M2016216
[59] Paris P, Erdogan F, 1963, A critical analysis of crack propagation laws. J. Basic Eng. 85, 528–533. https://doi.org/10.1115/1.3656900
[60] Fatemi A, Zeng Z, Plaseied A, 2003,Fatigue behavior and life predictions of notched specimens made of QT and forged microalloyed steels, Int. J. Fatigue 2004, 26, 663–672. https://doi.org/10.1016/j.ijfatigue.2003.10.005
[61] Newman J, Phillips E, Swain M, 1999, Fatigue-life prediction methodology using small-crack theory. Int. J. Fatigue. 21, 109–119. https://doi.org/10.1016/S0142-1123(98)00058-9
[62] Mughrabi H, 2015, Microstructural mechanisms of cyclic deformation, fatigue crack initiation and early crack growth. Philos. Trans. R. Soc. Lond. Ser. A 373. https://doi.org/10.1098/rsta.2014.0132
[63] Boyer H, 1985, Atlas of Fatigue Curves, 1st ed, American Society for Metals: Materials Park, OH, USA,; ISBN 0871702142.
[64] Atzori B, Meneghetti G, Ricotta M, 2011, Analysis of the fatigue strength under two load levels of a stainless steel based on energy dissipation. Fract. Struct. Integrity 17, 15–22. https://doi.org/10.3221/IGF-ESIS.17.02
[65] Ben Fredj, N Ben Nasr M, Ben Rhouma A, Sidhom H, Braham C, 2004, Fatigue life improvements of the AISI 304 stainless steel ground surfaces by wire brushing. J. Mater. Eng. Perform. 13, 564–574. https://doi.org/10.1361/15477020420819
[66] Sakin R, 2018, Investigation of bending fatigue-life of aluminum sheets based on rolling direction. Alex. Eng. J. 57, 35–47. https://doi.org/10.1016/j.aej.2016.11.005
